SOLUTION: Hello! I would appreciate it if you could help me solve this word problem: Two candles of the same height are lit at the same time. The first is consumed in four hours, the seco

Algebra ->  Customizable Word Problem Solvers  -> Travel -> SOLUTION: Hello! I would appreciate it if you could help me solve this word problem: Two candles of the same height are lit at the same time. The first is consumed in four hours, the seco      Log On

Ad: Over 600 Algebra Word Problems at edhelper.com


    

Question 1208637: Hello! I would appreciate it if you could help me solve this word problem:
Two candles of the same height are lit at the same time. The first is consumed in four hours, the second in three hours. Assuming that each candle burns at a constant rate, how many hours after being lit was the first candle twice the height of the second?
Found 3 solutions by Shin123, josgarithmetic, timofer:
Answer by Shin123(626) About Me  (Show Source):
You can put this solution on YOUR website!
Note that the exact height of the candles doesn't matter, since the candles burn at a rate proportional to their height (and the candles both have the same height). So we can assign a value to the height. To make computations easier, let the common height be 12.
For the first candle, every hour, the height decreases by 12/4=3. Therefore, after x hours, the height would be 12-3x.
For the second candle, every hour, the height decreases by 12/3=4. Therefore, after x hours, the height would be 12-4x.
Now, we need to find the time such that the first candle had twice the height of the second. This gives us the equation 12-3x=2%2812-4x%29. Distributing the 2 on the right hand side gives 12-3x=24-8x. Adding 8x to both sides now gives 12%2B5x=24. Subtracting 12 from both sides gives 5x=12. Finally, dividing both sides by 5 gives x=12%2F5. Therefore, the answer is 12%2F5 hours.

Answer by josgarithmetic(39630) About Me  (Show Source):
You can put this solution on YOUR website!
CANDLE          BURN RATE      TIME         LENGTH of CANDLE

First           d/4             x             d-(d/4)x

Second          d/3             x             d-(d/3)x

Question seems to need the "length of candles" to be as d-%28d%2F4%29x=2%28d-%28d%2F3%29x%29.

If divide left and right by d, then 1-x%2F4=2%281-x%2F3%29;
1-x%2F4=2-2x%2F3
-x%2F4=1-2x%2F3
2x%2F3-x%2F4=1
multiply left and right sides by 12;
8x-3x=12
5x=12
x=12%2F5
and this is 2 and two-fifths hours

2%262%2F5=2%2624%2F60 or two hours twenty-four minutes.

Answer by timofer(106) About Me  (Show Source):
You can put this solution on YOUR website!
You can take the original length of each candle to both be a unit of 1, for 1 candle length. Then for some expected time, since both are started at the same time, candle #1 will be 1-%281%2F4%29x and candle #2 will be 2%281-%281%2F3%29x%29.

You would have then 1-x%2F4=2%281-x%2F3%29.
Simplify this and solve for the time, x.